{"id":"https://openalex.org/W7140170667","doi":"https://doi.org/10.48550/arxiv.2603.21514","title":"Evaluating Power Flow Manifold from Local Data around a Single Operating Point via Geodesics","display_name":"Evaluating Power Flow Manifold from Local Data around a Single Operating Point via Geodesics","publication_year":2026,"publication_date":"2026-03-23","ids":{"openalex":"https://openalex.org/W7140170667","doi":"https://doi.org/10.48550/arxiv.2603.21514"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.21514","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.21514","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.21514","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Zheng, Qirui","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zheng, Qirui","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Wu, Dan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Dan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Wolter, Franz-Erich","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wolter, Franz-Erich","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Geng, Sijia","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Geng, Sijia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10305","display_name":"Power System Optimization and Stability","score":0.8269000053405762,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10305","display_name":"Power System Optimization and Stability","score":0.8269000053405762,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10454","display_name":"Optimal Power Flow Distribution","score":0.13420000672340393,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.006000000052154064,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/operating-point","display_name":"Operating point","score":0.6852999925613403},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5728999972343445},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5415999889373779},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.5340999960899353},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.4952999949455261},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4797999858856201},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4528000056743622},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4480000138282776},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.39719998836517334}],"concepts":[{"id":"https://openalex.org/C22762622","wikidata":"https://www.wikidata.org/wiki/Q628904","display_name":"Operating point","level":2,"score":0.6852999925613403},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5799999833106995},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5728999972343445},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5415999889373779},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.5340999960899353},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.4952999949455261},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4797999858856201},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4528000056743622},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4480000138282776},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41519999504089355},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.39719998836517334},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3937999904155731},{"id":"https://openalex.org/C176605952","wikidata":"https://www.wikidata.org/wiki/Q827674","display_name":"Phasor","level":4,"score":0.38420000672340393},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.37560001015663147},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3594000041484833},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35580000281333923},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34209999442100525},{"id":"https://openalex.org/C2986056383","wikidata":"https://www.wikidata.org/wiki/Q556030","display_name":"Power flow","level":4,"score":0.3231000006198883},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.32260000705718994},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.3111000061035156},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.30079999566078186},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.2994999885559082},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29260000586509705},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.29260000586509705},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.2921000123023987},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.2791999876499176},{"id":"https://openalex.org/C50429861","wikidata":"https://www.wikidata.org/wiki/Q3554830","display_name":"Stable manifold","level":2,"score":0.2711000144481659},{"id":"https://openalex.org/C181361822","wikidata":"https://www.wikidata.org/wiki/Q556030","display_name":"Power-flow study","level":4,"score":0.2671999931335449},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25999999046325684},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.21514","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.21514","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.21514","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.21514","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.9068042039871216,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"widespread":[1],"adoption":[2],"of":[3,27,82,120,133,140,158,187],"renewable":[4],"energy":[5],"poses":[6],"a":[7,11,24,28,41,64,79,86,116,155,162],"challenge":[8],"in":[9,15,102],"maintaining":[10],"feasible":[12,25],"operating":[13,88,164],"point":[14,165],"highly":[16],"variable":[17],"scenarios.":[18],"This":[19],"paper":[20,62],"demonstrates":[21],"that,":[22],"within":[23],"region":[26],"power":[29,37,54,66,75,105,122,173],"system":[30],"that":[31,70,139,154],"meets":[32],"practical":[33],"stability":[34],"requirements,":[35],"the":[36,73,103,112,121,131,141,148,170,185,188],"flow":[38,67,76,106,123,174],"equations":[39],"define":[40],"smooth":[42],"bijection":[43],"between":[44],"nodal":[45,52],"voltage":[46],"phasors":[47],"(angle":[48],"and":[49,51,95,127],"magnitude)":[50],"active/reactive":[53],"injections.":[55],"Based":[56],"on":[57],"this":[58,61],"theoretical":[59],"foundation,":[60],"proposes":[63],"data-based":[65,150],"evaluation":[68,151],"method":[69],"can":[71],"imply":[72,169],"associated":[74,104,172],"manifold":[77,107],"from":[78,92],"limited":[80],"number":[81,157],"data":[83],"points":[84],"around":[85,161],"single":[87,163],"point.":[89,114],"Using":[90],"techniques":[91,146],"differential":[93],"geometry":[94],"analytic":[96,109],"functions,":[97],"we":[98],"represent":[99],"geodesic":[100],"curves":[101],"as":[108],"functions":[110],"at":[111],"initial":[113],"Then,":[115],"special":[117],"algebraic":[118],"structure":[119],"problem":[124],"is":[125,166],"revealed":[126],"applied":[128],"to":[129,138,168],"reduce":[130],"computation":[132],"all":[134],"higher-order":[135],"partial":[136],"derivatives":[137],"first-order":[142],"ones.":[143],"Integrating":[144],"these":[145],"yields":[147],"proposed":[149,189],"method,":[152],"suggesting":[153],"small":[156],"local":[159],"measurements":[160],"sufficient":[167],"entire":[171],"manifold.":[175],"Numerical":[176],"cases":[177],"with":[178],"arbitrary":[179],"directional":[180],"variations":[181],"are":[182],"tested,":[183],"certifying":[184],"efficacy":[186],"method.":[190]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-03-25T00:00:00"}
